[Zhong-Qi, M. A.] Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; [Yang, C. N.] Tsinghua Univ, Inst Adv Study, Beijing 100084, Peoples R China
; [Yang, C. N.] Chinese Univ Hong Kong, Inst Theoret Phys, Hong Kong, Hong Kong, Peoples R China
Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.